Should my character face y-forward?
those shortcuts activate view alignment modes named "front" and "back" 



so I can't see why you feel they could be wrong, even if those are just names, and you can choose whatever (even to work not aligned to anything, but of course it helps...)

that said, some symmetry related tool considers the default (sometimes the only possible) symmetry around X axis, so that the object shape is considered mirrored on the +Y and -Y axis

This is clearly the case of "humanoid" features (like a face) so it seems to be considered the best choice, imho.